To determine the total cost \( c \) that Vicky paid for the oranges, we need to multiply the number of pounds of oranges she bought by the cost per pound.
Vicky bought \( 3 \frac{1}{2} \) pounds of oranges, which can be converted to an improper fraction:
\[ 3 \frac{1}{2} = \frac{7}{2} \text{ pounds} \]
The cost per pound is \( 3.90 \) dollars.
So, the total cost \( c \) can be calculated as:
\[ c = \text{(number of pounds)} \times \text{(cost per pound)} = \left(\frac{7}{2}\right) \times 3.90 \]
To find the equation that represents this scenario, when we multiply the number of pounds by the cost per pound, we can set it up as:
\[ c = \frac{7}{2} \times 3.90 \]
To express this relation using an equation, we can rearrange it to isolate \( c \):
The total cost in terms of the price per pound and pounds purchased is:
\[ c = 3.90 \times \frac{7}{2} \]
This doesn't exactly match any of the response formats provided, so let's check the responses:
- \( \frac{c}{3.90} = 3.5 \) - Incorrect
- \( \frac{3.90}{3.5} = c \) - Incorrect
- \( \frac{c}{3.5} = 3.90 \) - Incorrect
- \( 3.90c = 3.5 \) - Incorrect
None of the provided options correctly represent the equation for the total cost.
To calculate the total cost:
\[ c = \frac{7}{2} \times 3.90 = 3.5 \times 3.90 = 13.65 \]
Thus, Vicky paid \( 13.65 \).
So the equation for total cost Vicky paid for the oranges should be:
\[ c = 3.90 \times 3.5 \]
And the correct total amount Vicky spent is \( 13.65 \), but this should also be noted that there is no correct answer listed in the options.